use depth-first search to find a spanning tree of each ofthese graphs.a) w6 (see example 7 of section 10.2), starting at thevertex of degree 6b) k5c) k3,4, starting at a vertex of degree 3d) q3
Answers
a) Spanning tree of W6 (starting at degree 6 vertex) using depth-first search: 6-1-2-3-4-5. b) Spanning tree of K5 using depth-first search: Any spanning tree will do since K5 is a complete graph. c) Spanning tree of K3,4 (starting at degree 3 vertex) using depth-first search: 3-1-2-4-5-6-7. d) Spanning tree of Q3 using depth-first search: Any spanning tree will do since Q3 is a cycle graph.
a) To find a spanning tree of graph W6 (Example 7 of Section 10.2) starting at the vertex of degree 6, we can use the depth-first search algorithm as follows:
Start at the vertex of degree 6.
Mark it as visited.
Choose an unvisited adjacent vertex and move to it.
Repeat steps 2 and 3 until all vertices have been visited or there are no more unvisited adjacent vertices.
Backtrack to the previous vertex if there are no more unvisited adjacent vertices.
Continue the process until all vertices have been visited.
b) To find a spanning tree of graph K5, we can use the depth-first search algorithm as follows:
Choose any vertex as the starting point.
Mark it as visited.
Choose an unvisited adjacent vertex and move to it.
Repeat steps 2 and 3 until all vertices have been visited or there are no more unvisited adjacent vertices.
Backtrack to the previous vertex if there are no more unvisited adjacent vertices.
Continue the process until all vertices have been visited.
c) To find a spanning tree of graph K3,4 starting at a vertex of degree 3, we can use the depth-first search algorithm as follows:
Start at the vertex of degree 3.
Mark it as visited.
Choose an unvisited adjacent vertex and move to it.
Repeat steps 2 and 3 until all vertices have been visited or there are no more unvisited adjacent vertices.
Backtrack to the previous vertex if there are no more unvisited adjacent vertices.
Continue the process until all vertices have been visited.
d) To find a spanning tree of graph Q3, we can use the depth-first search algorithm as follows:
Choose any vertex as the starting point.
Mark it as visited.
Choose an unvisited adjacent vertex and move to it.
Repeat steps 2 and 3 until all vertices have been visited or there are no more unvisited adjacent vertices.
Backtrack to the previous vertex if there are no more unvisited adjacent vertices.
Continue the process until all vertices have been visited.
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Related Questions
An algorithm will be used to count how many numbers in a list are multiples of either 5 or 10. For the list of [5, 3, 2, 10, 20, 7], it should count 3 numbers (5, 10, 20). There are two proposals for the algorithm: Algorithm 1: Set value of count to 0. Iterate through each number in the list. If the current number is a multiple of 5 and a multiple of 10, increment count by 1. Algorithm 2: Set value of count to 0. Iterate through each number in the list. If the current number is a multiple of 5, increment count by 1. Then, if the current number is a multiple of 10, increment count by 1.
Answers
Algorithm 2 is the better proposal for this problem.
The reason for this is because of the specific nature of the problem statement.
The prompt calls for a count of the numbers that are multiples of either 5 or 10. However, Algorithm 1 only counts the numbers that are multiples of both 5 and 10.
This means that Algorithm 1 will not capture all the relevant numbers in the list, thus leading to incorrect results.
On the other hand, Algorithm 2 correctly counts all the numbers that are multiples of either 5 or 10. This is because it checks for multiples of 5 first and increments count if it finds a multiple.
Then, it checks for multiples of 10 and increments count again if it finds a multiple. By doing this, Algorithm 2 correctly captures all the relevant numbers in the list, thus leading to correct results.
Overall, Algorithm 2 is the better proposal for this problem.
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Problem
Which set of coordinates are located on line segment IK?
A.) (5,3)
B.) (7,6)
C.) (6,4)
D.) (6,9)
Answers
A point is on a line if the point is given by the equation or function of the line
The set of coordinates that is located on the line segment IK is (6 ,4)
C.) (6, 4)
Reason:
Coordinates of point I = (4, 4)
Coordinates of point K = (8, 4)
Given that the y-coordinate value of the two points on the line IK are the same, (both 4) the line IK is an horizontal line and the coordinate of a point on IK should have a y-value of 4
Therefore, the correct option is the point (6, 4)
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please answer, i have 5 mins
Use each of these rules to create 4 ordered pairs using the two sequences.
The first rule is add 12, then divide by 2, starting from 4.
The second rule is multiply by 2, then subtract 2, starting from 3.
Which table shows the 4 ordered pairs created using the two sequences?
A table with three columns. The first column is labeled rule 1, the second column is labeled rule 2, and the third column is labeled ordered pair. There are four rows below the heading row. Under column rule 1 are the numbers zero, four, six, and seven. Under column rule 2 are the numbers three, five, nine, and seventeen. Under the column labeled ordered pair are zero and three, four and five, six and nine, and seven and seventeen.
A table with three columns. The first column is labeled rule 1, the second column is labeled rule 2, and the third column is labeled ordered pair. There are four rows below the heading row. Under column rule 1 are the numbers two, six, eight, and nine. Under column rule 2 are the numbers two, four, ten, and twenty-eight. Under the column labeled ordered pair are two and two, six and four, eight and ten, and nine and twenty-eight.
A table with three columns. The first column is labeled rule 1, the second column is labeled rule 2, and the third column is labeled ordered pair. There are four rows below the heading row. Under column rule 1 are the numbers four, eight, ten, and eleven. Under column rule 2 are the numbers three, four, six, and ten. Under the column labeled ordered pair are four and three, eight and four, ten and six, and eleven and ten.
A table with three columns. The first column is labeled rule 1, the second column is labeled rule 2, and the third column is labeled ordered pair. There are four rows below the heading row. Under column rule 1 are the numbers six, eight, twelve, and twenty. Under column rule 2 are the numbers one, eight, twenty-two, and fifty. Under the column labeled ordered pair are six and one, eight and eight, twelve and twenty-two, and twenty and fifty.
Answers
Ordered pairs must be placed in the following order: (6, 1), (8, 8), (12, 22). (20, 50). The right answer is D.
What is arithmetic?According to the assertions, it deals with a number of operations in mathematics.
For the first series, let the number be x, and for the second, let it be y.
The first rule is to multiply by 2, then, beginning with 6, remove 4.
The sequence can be written as 6 is the first number: = 2x - 4
next number = 2(6) - 4
= 12-4
= 8
The following phrase is thus 8. The following two terms can be written as 12 and 20.
Values of x = 6, 8, 12, 20
The second rule is to add three and then multiply by two, counting backward from one.
= (y + 3)2
First term = 1
Next term = (1 + 3)2
= 8
The next two words can be acquired in a similar manner.
y = 1, 8, 22, 50
Therefore, ordered pairs must be placed in the following order: (6, 1), (8, 8), and (12, 22). (20, 50). The right answer is D.
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Correct question:
The first rule is to multiply by 2, then subtract 4 starting from 6. The second rule is to add 3, then multiply by 2 starting from 1. What are the first four ordered pairs using the two sequences?
A. (0, 0) (6, 1), (8, 2), (12, 22)
B. (6, 1), (10, 8), (14,22), (22, 50)
C. (6, 1), (8, 8), (12, 20), (20, 45)
D. (6, 1), (8, 8), (12, 22), (20, 50)
Graph the following equations.
X=1
Answers
Answer:
Vertical line that passes over 1 the x axis. (No y-intercept)
Step-by-step explanation:
There are 18 boys and 12 girls in a math class . What is the ratio of girls to total students
Answers
12:30
Answer:
The ratio of girls to total students is 12:30, which can be simplified to 2:5.
Step-by-step explanation:
You can express the ratio in different ways by using the same numbers, for example, you could say that for every 2 girls, there are 5 total students, or that for every 5 total students, 2 of them are girls.
the 150 residents of the town of wonderland were asked their age and whether they preferred vanilla, chocolate, or swirled frozen yogurt. the results are displayed next. chocolatevanillaswirl under 25 years old402015 at least 25 years old154020 what is the probability a randomly selected customer prefers chocolate given he or she is at least 25 years old?
Answers
If 150 town residents were asked about their age and yogurt , then the probability that a randomly selected customer prefers Swirl if age is at least 25 years old is 0.66 .
let X be = the selected customer that prefers swirled yogurt or is at least 25 years old ;
The sum of all the customers that are "at least 25 years old" = 21 + 30 + 24 = 75 ;
the sum of all the customers that " like Swirl Yogurt" is = 24 + 24 = 48 ;
the total number of residents = 150 students ;
So , the probability is calculated as : ( 75+48 -24)/150 = 0.66 .
Therefore , the required probability is 0.66 .
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The given question is incomplete , the complete question is
The 150 residents of the town of wonderland were asked their age and whether they preferred vanilla, chocolate, or swirled frozen yogurt. the results are displayed next.
Age Chocolate Vanilla Swirl
under 25 years old 22 29 24
at least 25 years old 21 30 24
What is the probability a randomly selected customer prefers Swirl Yogurt given he or she is at least 25 years old ?
Hunter wants to make money over the summer by selling lemonade. he has $50 in savings. he spends $20 on a pitcher and reusable cups. doing the math, he realizes that sugar, lemons, and water will cost $.75 per serving. what is the greatest number of cups that can be made before hunter runs out of his budget?
Answers
Hunter can make a total of 40 cups before he runs out of budget.
How much money does Hunter have to make lemonade?We know his total budget was $50 but he already spent $20 on a pitcher and cups.
$50 - $20 = $30This means the total of money just for the lemonade is $30.
How many lemonade cups can he make?To find this number divide the budget for lemonade by the cost of a lemonade cup $0.75.
$30 / $0.75 = 40Based on this, the total of cups he can make is 40 cups.
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Solve the system of equations by the addition method. x-6y=9 -x+ 2y = -5 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The solution is (Simplify your answer. Type an ordered pair.) OB. There are infinitely many solutions; {(x,y) |x-6y=9) or {(x,y)|-x+2y = -5}. OC. There is no solution; or Ø.
Answers
Main Answer:
OC. There is no solution; or Ø.
Explanation:
To solve the system of equations using the addition method, we need to eliminate one variable by adding or subtracting the equations. Let's consider the given system:
Equation 1: x - 6y = 9
Equation 2: -x + 2y = -5
If we add Equation 1 and Equation 2, the x terms cancel out, leaving -4y = 4. Dividing both sides by -4 gives y = -1.
Substituting the value of y = -1 into Equation 1, we have x - 6(-1) = 9, which simplifies to x + 6 = 9. Subtracting 6 from both sides yields x = 3.
Therefore, we find that x = 3 and y = -1. The solution is the ordered pair (3, -1).
However, if we look closely at the original equations, we can see that the coefficients of x in the two equations are opposite in sign. This implies that the lines represented by the equations are parallel and will never intersect. Hence, there is no common solution for the system of equations.
Therefore, the correct choice is OC. There is no solution; or Ø.
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The system of equations has a unique solution.
To solve the system of equations, we can use the addition method, also known as the elimination method. The goal is to eliminate one of the variables by adding the equations together.
Given the system of equations:
1) x - 6y = 9
2) -x + 2y = -5
To eliminate the x term, we can add equation 1 and equation 2 together. Adding the left sides gives us 0, and adding the right sides gives us 4y + 4. This simplifies to:
-4y = 4
Dividing both sides of the equation by -4, we find that y = -1.
Substituting this value of y into either equation, let's use equation 1, we have:
x - 6(-1) = 9
x + 6 = 9
x = 9 - 6
x = 3
Therefore, the solution to the system of equations is (3, -1), representing an ordered pair where x = 3 and y = -1.
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Find the most general antiderivative or indefinite integral. Check your answer by differentiation. [(5x¹45x+6) dx 14 [(5x¹4 - 5x+6) dx- 14 =
Answers
The most general antiderivative or indefinite integral of the given expressions is shown below:(5x⁴+5x+6)dx, and (5x⁴ - 5x+6) dx
We can confirm that our answers are correct by finding the derivative of the antiderivative and comparing it with the original expression that we had.Let us differentiate our first expression:
(5x⁴+5x+6)dx, and the second expression (5x⁴ - 5x+6) dxBoth expressions' derivatives match the original expressions. So we can say that our antiderivatives are correct.
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-4/0 divided by 5 11/14
Answers
Answer: undefined
Step-by-step explanation:
Need help solving these questions!! thank you :)
Answers
Answer:
1. 25+5c
2. -8y-16
3. (m+1)^9
4. -6a-15
5. 4y+12z
6. (2a+3b)^4
7. 23c
8. 8y+7x
9. 14a+16
10. 16m+16n
1. Luzcel real estate owns 8000 square meters of lot area and decides to construct two different styles of houses, B and C. The lot area of house B is 250 sq. m. and house C lot area is 200 sq. m. The construction engineer has a maximum of 6400 man-hours of labor for the construction. Let your variables be the number of units of house B and the number of units of house C to be constructed. a) Write an inequality which states that there are 8000 sq. m. of land available. b) A unit of house B requires 160 man-hour and a unit of house C requires 256 man-hour. Write an inequality that the engineer has at most 6400 man-hour available for construction. c) If material cost 600 thousand pesos for a unit of house B and 800 thousand for a unit of house C, write an inequality stating that the engineer has at least 12 million pesos to spend for materials. d) Labor cost 1.1 million pesos for constructing a unit of house B and 1.3 million pesos for constructing a unit of house C. If a unit of house B sells for 3.5 million and a unit of house C selis for 4 million, how many units of house B and house C should be constructed to obtain the maximum profit? Show the graph.
Answers
Inequality stating that there are 8000 sq. m. of land available: Let B be the number of units of house B and C be the number of units of house C.
Therefore,B+C ≤ 8000/200 [Reason: House C requires 200 sq. m. of land]⇒B+C ≤ 40b. Inequality that the engineer has at most 6400 man-hour available for construction:
160B + 256C ≤ 6400c
Inequality stating that the engineer has at least 12 million pesos to spend for materials:
600B + 800C ≤ 12000d
. Let us write down a table to calculate the cost, income and profit as follows:Units of house BLabor Hours per unit of house BUnits of house CLabor Hours per unit of house CTotal Labor HoursMaterial Cost per unit of house BMaterial Cost per unit of house CTotal Material CostIncome per unit of house BIncome per unit of house C
Total IncomeTotal ProfitBC=8000/200-B160CB+256C600000800000+256C12,000,0003,500,0004,000,0003,500,000B+C ≤ 40 160B + 256C ≤ 6400 600B + 800C ≤ 12000 Units of house B requires 160 man-hour and a unit of house C requires 256 man-hour.
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I need help ASAP, please help me
Answers
can someone explain how to do this :) im very confused
Answers
Answer:
the answer is 36q^7
Step-by-step explanation:
multiply the bases and add the exponents
Martin has read 40% of a book. He has 48 more pages to finish. How many pages are there in the book?
Answers
Answer: There are 80 pages in Martin's book.
48 pages = 60%
divide by six
8 pages = 10%
mulitiply by 10
80 pages = 100%
Hope this helps :)
work out the circumference of a circle 14cm take π to be 3.142
Answers
The circumference of the circle is approximately 87.964 cm.
To work out the circumference of a circle, we use the formula:
C = 2πr
Where C is the circumference, π (pi) is a mathematical constant approximately equal to 3.14159, and r is the radius of the circle.
In this case, we are given the radius of the circle as 14cm and π is 3.142. So, we can substitute these values into the formula to get:
C = 2 x 3.142 x 14
C = 87.964
Therefore, the circumference of the circle is approximately 87.964 cm.
The formula for the circumference of a circle, as you mentioned, is C = 2πr. This formula relates the circumference of a circle to its radius, where the radius is the distance from the center of the circle to its edge.
In order to use this formula, you first need to know the value of the radius.
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Differentiate. F(y) = 1/ y^2 − 9 /y^4 (y + 5y^3)
Answers
To differentiate F(y) = 1/ y^2 − 9 /y^4 (y + 5y^3), we need to use the quotient rule of differentiation. Your answer: F'(y) = -2y^(-3) - (12y^(-5) + 60y^(-2))(y + 5y^3)
The quotient rule states that the derivative of a quotient of functions is equal to the numerator's derivative multiplied by the denominator minus the denominator's derivative multiplied by the numerator, all divided by the denominator squared.
Using this rule, we can find the derivative of F(y) as follows:
F'(y) = [(d/dy) (1/ y^2) * (y^4(y + 5y^3)) - (d/dy) (y^4(y + 5y^3)) * (1/ y^2)] / (y^4(y + 5y^3))^2
Simplifying this expression, we get:
F'(y) = [(-2y^3(y + 5y^3))/(y^4(y + 5y^3))^2 - (y^4(1 + 15y^2))/(y^2(y^4(y + 5y^3))^2)]
= [(-2y^3(y + 5y^3)) - (y^4(1 + 15y^2))] / (y^6(y + 5y^3))^2
= (-2y^4 - 10y^6 - y^4 - 15y^6) / (y^6(y + 5y^3))^2
= (-3y^4 - 25y^6) / (y^6(y + 5y^3))^2
Therefore, the derivative of F(y) is F'(y) = (-3y^4 - 25y^6) / (y^6(y + 5y^3))^2.
To differentiate the function F(y) = 1/y^2 - 9/y^4 (y + 5y^3), you can apply the power rule and the chain rule.
Your answer: F'(y) = -2y^(-3) - (12y^(-5) + 60y^(-2))(y + 5y^3)
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Let m = x^2 - 5
Which equation is equivalent to (x^2-5)^2 - 3x^2 + 15= -2 in terms of m ?
A m^2+3m+2=0
B m^2-3m+17=0
C m^2-3m+2=0
D m^2+3m+17=0
Thanks!
Answers
The equivalent equation to the (x² - 5)² - 3x² + 15 = -2 in form of 'm' is given by option c. m² -3m + 2 = 0.
The equation is equal to,
(x² - 5)² - 3x² + 15 = -2
let the value of m be equals to x² - 5.
Simplify the equation we have,
⇒ ( x² - 5 )² - 3x² + 15 = -2
Take '3' common factor from the 3x² + 15 so that it get convert into x² - 5 we get,
⇒ ( x² - 5 )² - 3 (x² - 5 ) = -2
Now replace x² - 5 by m to get the equivalent equation,
⇒ ( m )² - 3 (m ) = -2
⇒ m² -3m + 2 = 0
Therefore, the equivalent equation to the given equation is written as option c. m² -3m + 2 = 0.
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A certain company employs 6 senior officers and 4 junior officers. If a committee is to be created that is made up of 3 senior officers and 1 junior officer, how many different committees are possible
Answers
Answer:
80
Step-by-step explanation:
A certain company employs 6 senior officers and 4 junior officers. If a committee is to be created that is made up of 3 sr officers and 1 jr officer, how many different committees are possible?
8
24
58
80*
210
I initially got this one wrong, but after I saw the answer which is 80, I was able to solve it. But im not sure if this is the proper way of solving it, or if someone can suggest a more efficient way of solving it?
This is what I did, which was wrong:
Sr Officers + Jr Officers
(6!/3! 3! = 20) + (4!/3! = 4) = 24
It seems like the correct answer is:
Sr Officers X Jr Officers
(6!/3! 3! = 20) x (4!/3! = 4) = 80
If this is the most efficient way of solving, when do you know when to add them as opposed to multiplying them in this case?
In the first half of last year, a team won 60 percent of the games it played. In the second half of last year, the team played 20 games, winning 3 of them. If the team won 50 percent of the games it played last year, what was the total number of games the team played last year?
A) 60
B) 70
C) 80
D) 90
E) 100
Answers
The total number of games the team played last year was 80 (option C). In the first half of the year, the team won 60 percent of their games, indicating that they won 6 out of every 10 games played.
In the second half of the year, the team played 20 games and won 3 of them. This means that in the second half, they won only 3 out of 20 games, which is equivalent to winning 15 percent of their games.
To find the overall percentage of games won, we can calculate the weighted average of the two percentages. Since the team won 50 percent of their games overall, we can assign equal weights to the first and second halves of the year. Therefore, the average winning percentage for the team would be the midpoint between 60 percent and 15 percent, which is (60% + 15%) / 2 = 37.5%.
Let's assume the total number of games played last year was x. Since the team won 37.5% of the games, they won 0.375x games. We can set up an equation based on the information given:
0.375x = 50% of x
0.375x = 0.5x
0.5x - 0.375x = 0
0.125x = 0
x = 0 / 0.125
x = 0
However, we have arrived at an invalid result. It seems there is an error in the information provided or the calculations made.
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Solve the inequality for x: x−1x−2≥0
Answers
Given:
Inequality is
\(\frac{x-1}{x-2}\ge0\)Required:
Solve the inequality.
Explanation:
We have inequality greater than or equal to zero.
So, this can happen only when both numerator and denominator positive or negative.
Fraction will be positive when x less than or equal 1 and when x greater than 2.
So, it is
\((-\infty,1]or(2,\infty)\)Answer:
Hence, option B is correct.
The perimeter of square is 24 meters. What is the length of one side of the square. Show your work
Answers
Answer:
6+6+6+6
Step-by-step explanation:
Perimeter of square is 24 m.
Perimeter of square = 4 × Side
\( \bf \implies \: \large \: 24 \: = \: 4 \: \times \: Side\)
\(\bf \implies \: \: Side \: = \: \frac{24}{4} \\ \)
\(\bf \implies \: \: Side \: = \: \cancel\frac{24}{4} \: ^{6} \\ \)
\(\bf \implies \: \: Side \: = \: 6 \: meters\)
I need help what do I have to do plz if you don’t know the answer don’t write nothing thank you
Answers
Determine the solution to the equation. 8+4x=2x+8+2x A Infinite B One Solution C No Solution
Answers
After solving the given equations the answer is an Infinite solution. Hence, option A is correct
What is an equation?Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.
This relationship is illustrated by the left and right expressions being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.
As per the given equation in the question,
8 + 4x = 2x + 8 + 2x
Firstly, let's write the given equation in a simplified manner,
8 + 4x = 8 + 4x
As we can see that LHS = RHS, which means that both equations are the same then which means they will give infinite solutions.
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-3a+6b=a+4b I need to solve this please.
Answers
Answer:
a*2=b
Or
a=0, b=0
Step-by-step explanation:
if a=0 and b=0, then 0=0, it'd be correct, but I'm sure that's not the answer they intend you to pick. You should still put that as one of the answers, however.
-3a+6b=a+4b
+3a +3a
6b=4a+4b
-6b -6b
0=4a-2b
/2 /2 /2
0=2a-b
so, we now know that b is twice the amount that a is, and actually, that's the solution for the entire thing.
So, the answer is a*2=b, because the equation works for any set of numbers, as long as it follows this rule.
please help! find QPR
Answers
Answer:
m∡QPR = 25°
Step-by-step explanation:
solve for 'x':
8x + 7 + 9x + 16 = 40
17x + 23 = 40
17x = 17
x = 1
m∡QPR = 9(1) + 16
m∡QPR = 25°
PLEASE HELP ASAP if you can please tell me what goes in each box!
Answers
Answer:
:< :< :< :< :< :< :< ?
Step-by-step explanation:
Factor 2mp - 3p - 4m - 6
Answers
Answer: mp • (3m3 + 8m2p - 2p2)
Step-by-step explanation:
3m4p + 8m3p2 - 2mp3 = mp • (3m3 + 8m2p - 2p2)
8.2 Factoring 3m3 + 8m2p - 2p2
The regression line is called the least squares line because it is the line that results in the __________ sum of the squared __________.
Answers
Answer:
Smallest
Vertical deviations
Step-by-step explanation:
As part of a science experiment, a student recorded 10 measurements of the temperature of a liquid. One of the measurements was an outlier when compared with the other 9 measurements. Which of the following must be true about the 9 measurements, excluding the outlier, when compared with the 10 measurements? (Note: An outlier is any number that is greater than the upper quartile or less than the lower quartile by at least 1.5 times the interquartile range.) (A) The median of the 9 measurements is less than the median of the 10 measurements. (B) The median of the 9 measurements is greater than the median of the 10 measurements. (C) The maximum of the 9 measurements is less than the maximum of the 10 measurements. (D) The maximum of the 9 measurements is greater than the maximum of the 10 measurements. (E) The standard deviation of the 9 measurements is less than the standard deviation of the 10 measurements.
Answers
Among the given options, (C) The maximum of the 9 measurements is less than the maximum of the 10 measurements must be true about the 9 measurements, excluding the outlier, when compared with the 10 measurements.
An outlier is defined as a measurement that significantly deviates from the other measurements in a data set.
In this case, one of the measurements among the 10 is identified as an outlier.
When comparing the remaining 9 measurements with the entire set of 10 measurements, the maximum value of the 9 measurements cannot exceed the maximum value of the 10 measurements because the outlier, by definition, exceeds the upper quartile or lower quartile by at least 1.5 times the interquartile range.
It is important to note that the median of the 9 measurements can be either greater than or less than the median of the 10 measurements, depending on the specific values of the measurements.
The presence of the outlier does not necessarily determine the relationship between the medians of the two sets.
Similarly, the standard deviation of the 9 measurements may or may not be less than the standard deviation of the 10 measurements.
The inclusion or exclusion of the outlier can have an impact on the standard deviation calculation, but it is not guaranteed to be lower or higher in either case.
Therefore, among the given options, the only statement that must be true is (C) The maximum of the 9 measurements is less than the maximum of the 10 measurements.
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